Chi-Square Test - Background

A chi-square test is employed when one wishes to determine if a sample fits some theoretical distribution. In a chi-square test, each of the observed values are compared to the value that would be expected given a theoretical distribution.

Once calculated, the chi-square statistic is compared to a critical value, which is determined using the number of categories, the chosen level of significance (typically a = 0.05), and a critical value table. If the statistic calculated is less than the critical value, the sample fits the theoretical distribution. Otherwise, there is a significant difference between the observed and expected.